A digital bearer transaction is one where a cryptographically secure value-object, issued and underwritten by a third party, is exchanged between the two parties in a trade, typically over a public internetwork.  The object, when passed in trade for something else of value, executes, clears, and settles the transaction instantaneously, securely, and, usually, anonymously. And, at considerable savings in transaction cost compared to "book-entry" transactions, such as credit and debit cards, checks, and modern securities clearing methods.
It is estimated that $100 billion in transactions are being executed on the internet annually. 40% of all retail stock trades are now executed from the net, for instance. If it's possible to properly call a credit card transaction transmitted under Secure Socket Layer to be settled and cleared on the net itself, then an estimated maximum of $10 billion of those transactions, 10%, are actually cleared and settled on the net, with marginal market share to other transaction protocols. By comparison, $3 trillion in foreign exchange transactions are executed, cleared and settled every day, using standard book-entry processes.
There are electronic check and debit protocols in experimental development, but, as transaction settlement time tends towards the instantaneous, the more cost, security, and non-repudiation advantages there are for digital bearer settlement. It is not unreasonable to see how transaction costs can be reduced enormously by digital bearer settlement, possibly by several orders of magnitude over any analogous book-entry method. It is completely conceivable that digital bearer transactions, of all kinds and sizes, from macrobonds to micropayments, will be executed, cleared, and settled on ubiquitous global internetworks, and will become the dominant transaction mechanism over time on those networks, and, by extension, in the global economy in general.
It may happen sooner than we can imagine. Electronic book-entry settlement itself is only 40 years old at best, and internet financial cryptography and digital bearer settlement are much more a phenomenon of collapsing microprocessor prices than electronic book-entry settlement ever was.

Our current system of so-called "book-entry" transaction settlement was invented in order to handle the problems caused by remote transaction execution and the subsequent need to physically exchange bearer certificates for settlement. It can easily be said that the entire structure of modern capital markets has been built around this communication architecture of hierarchically "wired" charts of accounts. At the top of all markets is some kind of geodesic "face-to-face" auction market, be it an exchange of some sort, or an open-outcry pit, or, more recently, overgrown bulliten-boards like the NASDAQ or Reuter's currency system. But, until a trade gets to where it is actually executed, it's either climbing up or down this extensive financial ziggurat we've built to move our money around. And, especially after the trade is executed, it still has to clear and settle in the same kind of system.
All of this bookeeping and shuffling of paper takes a long time. Transactions requiring bearer settlement would take weeks, and then, with improvements in transportation (Brinks became an air cargo business as well), days, to settle. Within living memory, even pure book-entry transactions on the New York Stock Exchange would take up to 5 business days to settle, and that was with all stock certificates locked down in a vault at the Depository Trust Company in New York. NYSE transactions now clear with offsetting accounts on the respective books of the buyer, seller, and the DTC, and they settle when the buyer's funds arrive in the seller's bank account.
Book-entry settlement is not just confined to transactions in the financial markets. Virtually all forms of money except physical cash is in book-entry form now.

A check is a request to your bank to move money up, and then back down, another financial ziggurat of offsetting book-entries called the automated clearinghouse system, eventually landing in the bank account of the person you wrote the check to.

A credit card transaction is simply an instruction to borrow money from a bank, or from Diner's Club or American Express, and send it over the financial clearing ziggurat to the vendor in question, with your implicit promise to pay the lender back later.
Even a "foreign" ATM transaction is effectively a loan settled over the finanancial ziggurat. That's what those "inflated" ATM fees pay for, for the most part: the time value of the money "lent" to you by the owner of the machine plus, the cost of running the machine itself, and the opportunity cost of not lending it elsewhere.

Even though global currency transactions are executed geodesically -- directly between bank to bank -- the transactions still settle on a book-entry basis over SWIFT, or other international funds transfer systems, and thus move hierarchically to settle, especially for smaller banks. 



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